The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month: The standard deviation of this distribution is ___.
A) 1.800
B) 1.345
C) 1.400
D) 4.000
E) 1.457

Question

The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month:  The standard deviation of this distribution is ___.
A) 1.800 
B) 1.345 
C) 1.400 
D) 4.000 
E) 1.457

Quizplus · Accepted Answer

To find the standard deviation, we first need to find the mean, which can be calculated as follows:

Mean = Σ (x*p(x)) 
where x is the number of accidents and p(x) is their respective probabilities.

Mean = (2*0.3) + (3*0.2) + (4*0.1) + (5*0.2) + (6*0.1) = 3.7

Next, we can calculate the variance:

Variance = Σ [(x - mean)^2 * p(x)]

Variance = [(2-3.7)^2*0.3] + [(3-3.7)^2*0.2] + [(4-3.7)^2*0.1] + [(5-3.7)^2*0.2] + [(6-3.7)^2*0.1]

Variance = 1.440

Finally, we take the square root of the variance to find the standard deviation:

Standard deviation = sqrt(variance) = sqrt(1.440) = 1.345.

Therefore, the answer is B.

The Manager of a Home Improvement Store Is Studying the Number